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Review of Applied Economics, Vol. 4, No. 1-2, (January-December 2008) : 113-124
CAN HIPCs USE HYPER-INCENTIVES?
Gordon Douglas Menzies*
Hyper-incentive contracts (Menzies 2004) can be used to pursue humanitarian goals (providing
a safety net) while allowing creditors to offer innovative repayment friendly contracts to debtors
(eliminating a debt overhang). Both the contract of Krugman (1988) and the hyper-incentive
contract are illustrated with some calculations based on current Highly Indebted Poor Countries
(HIPCs). The outcomes for the two contracts are similar, but the twelve countries examined
could each benefit by an average amount of $US2002 100 million under a hyper-incentive contract.
JEL Classification: F34.
Keywords: Debt overhang; Debt forgiveness; Hyper incentive contract.
INTRODUCTION
The turbulent events of the 1970s, followed by the high interest rate regime of the Volker
deflation, ushered in the modern third world debt crisis. For the poorest countries, most of the
debt was sovereign, and owed to OECD governments and international agencies. Rescheduling
occurred at the Paris Club of creditors. If the club believed, usually on the say-so of the IMF,
that the country was making a significant adjustment effort, the debts would be rescheduled.
Initially, any rescheduling maintained the net present value of the debt, but by 1996 this
was abandoned as unrealistic. The IMF and the World Bank unveiled the HIPC initiative, whereby
very poor countries could apply for the writing down of sovereign debt, usually in concert with
other creditors. In 1999 HIPC debt-relief was tied to success in poverty reduction, and renamed
Enhanced HIPC. The overall level of assistance under Enhanced HIPC was also increased.
Finally, in 2005, the debt relief effort was tied to the Millennium Development Goals via the
Multilateral Debt Relief Initiative (IMF, 2007a and 2007b).
Alongside rapid developments in the world of policymaking, a literature on debt forgiveness
was emerging. The key question was how countries and their creditors could or should deal
with debt defaults. The answer partly depended upon the assumed motives of the creditors. One
strand of the literature assumed creditors forgive in order to maximize repayments, while the
other strand assumed creditors acted graciously.
As an example of the first strand, Debt Overhang models (Krugman 1988, and others1)
proposed a setup where the excess of output over an endogenous debt repayment was kept by
*
University of Technology, PO Box 123 Broadway 2007 NSW Australia, E-mail: [email protected]
114
Gordon Douglas Menzies
the debtor.2 Partial forgiveness gets the economy going, and helps the creditors recover debt.
Without it, the creditors hold the original claim over a stagnant economy, but receive little by
way of actual repayments. Krugman (1988) is explained in detail later.
More recently the winds of change have blown across the international community, and
this is reflected in the second strand of the literature. It is not uncommon now to find writers
assuming creditor graciousness. For example, Addison and Murshed (2003) write about situations
where debt forgiveness could be offered to stop civil wars, and, Cordella and Dell’Ariccia
(2002) consider a world where all aid (including debt relief) has the sole aim of promoting
effective social programs.
Naturally, the single instrument of debt forgiveness cannot achieve two goals, namely
maximal creditor returns and a target level of welfare for the indebted country. A recent proposal
(Menzies 2004) involves a contract where a debtor who clears a (partly forgiven) debt receives
an additional payment from the creditor, called a hyper-incentive. The hyper-incentive contract
ties these two strands together, in the spirit of the following quote from Jonathan Eaton:
‘The response to the debt crisis in poor countries should be framed in terms of overall foreign aid
objectives and policies. The argument for relief is primarily humanitarian...’
(Eaton 1990, page 45, my italics).
The hyper-incentive contract accepts this statement, while noting that primarily is not the
same as solely. Creditors guarantee debtors a minimum level of anticipated well-being, along
with a combination of forgiveness and cash bonuses (hyper-incentives) to maximize the creditor
payoffs. The aim is to pursue humanitarian goals to an appropriate degree, while allowing
creditors to offer innovative repayment friendly contracts to debtors.3 The level of debtor wellbeing offered by the creditor measures their ‘graciousness’.
This paper is organized as follows. Section 2 outlines the intuition of the hyper-incentive
contract. Section 3 extends the Krugman contract and the hyper-incentive contract within a
model to enable a calibration exercise in Section 4. Section 5 concludes.
THE INTUITION OF THE HYPER-INCENTIVE CONTRACT
The Krugman and hyper-incentive contracts are implicitly a solution to a moral hazard problem,
where the principal (the creditor) seeks to get the agent (the debtor) to act on their behalf.
Therefore, both contracts make most sense when the economic reform efforts of the debtor are
unobservable4, and effort and random influences combine together to produce a potential payment
to the creditor. The key question is; how much of this potential payment should the creditor
request in advance?
Krugman’s answer was to drop the requested payment to the point where the debtor has a
reasonable chance of clearing it. This gives the debtor good reason to exert effort, thereby
giving the creditor a good chance of collecting the reduced amount. The nature of the incentive
problem that Krugman addresses is shown in Figure 1. L is the amount of debt and x is the
output from which to pay that debt.5 Importantly, output x is influenced both by effort and some
unforecastable shock.
Can HIPCs Use Hyper-Incentives?
115
Figure 1
Debtor
payoff
Slope = 1
L
x
From the debtor’s point of view, an x outcome up to the point L does not yield a direct benefit.
That is, any extra output produced goes to the creditor, leaving a zero debtor payoff. Once the debt
is cleared, every extra unit of output is kept, so the marginal payoff for every unit of extra output
is unity. Since x is partly random, so that the debtor could end up on the flat or upward sloping
portions of the payoff schedule, the expected payoff of expending effort is decreasing in L. This
low expected payoff is the so called debt overhang. Krugman’s solution (Figure 2) is to drop the
required repayment (to A), thereby increasing the expected returns to effort.
Figure 2
Debtor
payoff
Slope = 1
A
L
x
Forgiveness
It is noteworthy that Krugman’s analysis does not allow the well being of the debtor nation
to be independently chosen – it simply drops out of the creditor’s maximization problem. There
are two worthwhile objectives – repaying creditors and providing a debtor safety net – but
forgiving debt, the only tool available, cannot accomplish both.
It is proved in the next section that introducing a cash bonus – a ‘hyper-incentive’ – to any
debtor that clears a tranche of reduced debt can achieve the twin goals. With a hyper-incentive
contract, the strategy is to target the debtor’s well-being by an appropriate amount of forgiveness,
but include a cash bonus adjustment (a hyper-incentive) to ensure that the debtor exerts the
optimal level of effort.
The hyper-incentive can motivate the optimal level of effort because the expected return to
producing an extra unit of output under the Krugman contract is a convex combination of zero
(on the flat portion) and unity (on the upward sloping portion of the Krugman contract). No
matter what level of forgiveness is chosen, the debtor benefit of a unit increment in output must
be less than unity, being a convex combination of zero and unity. However, the social benefit
(i.e. the combined creditor-debtor benefit) of a unit increment in output is clearly unity, which
is greater than the private benefit. Effort will therefore be underprovided in the Krugman contract.
Under a hyper-incentive contract, the slope of the upward-sloping portion of the benefit
schedule can be chosen to equate the (debtor’s) private return to effort to the social return. If it
is greater than unity, a convex combination of zero and this number can be made equal to unity
– the social benefit.
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Gordon Douglas Menzies
The size of the bonus depends on the debtor’s incentives. For countries requiring little
forgiveness (i.e., those not needing a large safety net), there is the problem that effort may go
unrewarded, so a large bonus is required. For countries requiring a lot of forgiveness (those needing
a large safety net) the remaining incentive problem is small, so the bonus can be as well.
These observations allow us to draw two types of hyper-incentive contracts – one for a
country experiencing relatively minor difficulties (requiring a low debtor safety net and little
forgiveness) and one for a country experiencing severe difficulties (requiring a high safety net
and lots of forgiveness). For output x*, the debtor keeps any output in excess the required
repayment (shown by the light line) plus a bonus depending upon how far the output exceeds
the forgiven debt (shown by the dashed vertical gap).
Figure 3
Low Safety Net
High Safety Net
Debtor
Payoff
(bold)
Slope = 1
x*
L
Slope = 1
x
x* L
x
= Lots of Forgiveness
= Little Forgiveness
These results are now outlined more formally.
A MODEL FOR COMPARING CONTRACTS
The following exposition follows Krugman (1988) and Menzies (2004). However, one major
extension is that output is defined such that effort is pre-multiplied by a parameter b, which
facilitates the calibration exercise of Section 4.
Period 1: A Creditor lends $L and announces the required repayment (a) for the second
period. After observing a the debtor exerts effort e, with cost of effort C(e)= e2/2l.
Period 2: Nature draws a uniformly distributed error h over (–h, h). This combines with
effort to produce debtor output:
x = be + h
and
E(x) = be.
(1)
The parameter b allows measured effort to be mapped onto output, which is important in Section
4. If x > a the debtor keeps the excess of output over the repayment, i.e., x – a. If not, Krugman
assumes a gunboat technology transfers x to the creditor. The expected value of the debtor’s
‘limited liability’ payoff is.
P = x – a If
E(P) =
be + h
òa
= 0 If
x>a
æ 1 ö
( x - a) ç ÷ dx
è 2h ø
x£a
Can HIPCs Use Hyper-Incentives?
117
To find the e that maximizes expected debtor utility, E(Ud), set the marginal expected private
payoff (MEPP) equal to marginal cost.
E(Ud) = E(P) – C(e)
(2)
b (b e + h - a)
e
= MEPP = MC =
l
2h
Þ
e=
lb (h - a)
2h - b2 l
S.O.C. b2l – 2h < 0
(3)
The equation for e can be interpreted as the debtor reaction function. For a given a, the effort
choice maximizes debtor utility. Creditors face a tradeoff; more forgiveness (lower a) increases
effort and the chance of collecting a, but a is also a cap on what can be collected. The optimal
e (contingent on a) is substituted into expected creditor utility.
E(Uc) = e – E(P) – L
(4)
The value of a arising from the maximization of E(Uc) can be less than L, implying debt
forgiveness.
a=b
b2 l 2
+ h - b2 l = b eKrugman + h - b2 l = x max - b2 l
2h
(5)
As discussed by Krugman (1988), the creditor asks for the maximum possible output from the
debtor (calculated at Krugman’s optimal level of effort) less a forgiveness discount that is
increasing in both b and l. For higher marginal impacts of effort on output, the creditor’s effort
increasing forgiveness discount is more beneficial to the creditor, and, for lower debtor effort
costs (higher values of l) the benefits of forgiveness are likewise more easily realized.
Optimal a is substituted into (3), giving the optimal value of e:
eKrug= bl (b2l/[2h]).
(6)
The second order condition in (3) implies that optimal e is less than bl. This is important,
as we can see from adding the expected utilities of the creditor and debtor together. This is
called V, for the total expected value of output net of effort:
V = be -
e2
-L
2l
Þ
¶V
e
=b- =0
¶e
l
Þ
e = bl
(7)
The contract fails to maximize V, because debtor private benefit is too low, as was noted in
Section 2.
The hyper-incentive contract allows the debtor payoff to have an incentive parameter.
Repayment required is now a/b, (where a need not take the same value as it does in the Krugman
contract).
P = bx - a
E ( P) = ò
be + h
a/ b
If
1
(bx - a) æç ö÷ dx = 0 If
è 2h ø
x > a / bü
ï
ý
x £ a / bï
þ
(8)
118
Gordon Douglas Menzies
The optimal e is then obtained by differentiation.
e=
lb (bh - a)
(9)
2h - bb2 l
Note that the optimal e depends upon both a and b. It is decreasing in a and increasing in b.6
Next, the sum of the utilities is differentiated with respect to b.
V = b e [ b] -
1
e[b]2 - L
2l
¶V
e[b] ö
æ
= e¢ [ b ] ç b ÷=0
¶b
l ø
è
Þ e[b] = bl
(10)
The second order condition holds at the optimum (i.e., given that b – e[b]/l = 0). The
parameter b is chosen by the creditor to make it privately optimal for the debtor to set e equal to
bl, and a is chosen to attain a fixed reservation utility U for the debtor. The independent choice
of the reservation utility is possible because there are now two instruments (a/b and b) available.
The full solution thus involves equating (9) and (10), meeting the participation constraint with
equality
E (Ud) = E(P) –
e2
=U>0
2l
and solving. The resultant expressions for b and the threshold a/b are the key parameters of the
hyper incentive contract.
2h
ü
ï
b l + 2U ý
a / b = h - 2U ïþ
b=
2
(11)
The claims made above Figure 3 can now be justified. As the reservation utility U offered
to a country rises, a/b and b both fall (‘High Safety Net’ in Figure 3) and vice versa.
To work out the actual amount of the hyper-incentive paid to the exporter, we note that, in
reality, an exporter keeps the revenue from exports that exceed the debt repayment threshold
a/b, so this does not need to be ‘paid to’ the debtor by the creditor. All that remains to be paid
is the excess, for a realized value of x, say x*:
HICexcess=(x* – a/b) (b – 1)
(12)
Finally, it is noted that if the reservation utility offered to the debtor is the same as is available
under the Krugman contract then a switch from a Krugman contract to a hyper incentive contract
will, by construction, leave the debtor no worse off. However, since first-best effort (bl) is now
being exerted the size of V increases, and there is a surplus which can be divided between the
debtor and creditor.7 Quantifying the size of this surplus is the aim of the calibration exercise.
Can HIPCs Use Hyper-Incentives?
119
CALIBRATION
Including a effort function parameter b in the models of Krugman (1988) and Menzies (2004)
allows effort and output to be connected empirically. For the purposes of this exercise output
and effort will be defined as: the ratio of exports to GDP, and, the ratio of non-government
expenditure to GDP (both expressed in percentage terms).8 It is natural to use exports as the
output variable from which external debt obligations are paid, and the choice of non government
expenditures reflects the notion that, ceteris paribus, a reduction in the ratio of government
spending to GDP will lead to an increase in exports.
A standard Mundell-Fleming framework could provide the motivation for such a claim,
though reality is undoubtedly far more complex than the following simple diagram.9
Figure 4
(i = Interest rate, y = GDP)
i
LM
B
A
IS
y
An increase in the ratio of non-government spending to GDP is the same as a fall in
government spending, shown by the dashed line. If the point A represents full-employment,
then under a fixed rate regime (the norm for many poor countries) the economy will end up at
A in the final equilibrium.10 In the short run, monetary contraction takes the economy to B to
maintain the exchange rate peg. Deflation follows, expanding real money and pushes the LM
curve rightwards, and, depreciating the real exchange rate pushing the IS curve rightwards.
These forces of change continue until the initial equilibrium A is restored. At that point,
consideration of the identity GDP = C + I + G + X – M confirms that X – M must exactly offset
the fall in G (assuming C and I are functions of unchanged Y and i). All that is being asserted is
that part of this increase in X – M is due to an increase in X.
There is no requirement that the countries selected for this exercise be HIPCs, since the
Krugman setup does not distinguish between sovereign and private debt. However, given the
current interest in these countries, they are the natural choice.11
The required parameters for the calibration are b (the marginal impact of effort on output),
h (the upper and lower bound on the error h), and l (the cost of effort).
The first two parameters are relatively straightforward to quantify. An OLS regression of
exports on non-government spending (both as a percentage of GDP):
xi = b (100 – gi ) + ui
(g is %GDP public spending)
120
Gordon Douglas Menzies
gives b estimates for each country, and, a time series of residuals corresponding to each b
estimate for each country. If the residuals are then assumed to be an i.i.d. draw from a uniform
distribution, the maximum likelihood estimate for the bound h is just the maximum absolute
residual.12
For l it is assumed that the HIPC and Enhanced HIPC initiatives are forms of Krugman
debt forgiveness contracts, and that the observed levels of non government expenditure represent
optimal effort. This is certainly an ‘as if’ assumption, for two reasons.
First, many of these countries suffer severe problems in governance, calling into question
the basic assumption of rational action (though some might question this assumption for
developed country governments as well). More fundamentally, HIPC debt forgiveness ties the
level of forgiveness to the level of debt, aiming for ‘sustainable’ debt-to-export ratios. Krugman’s
model addresses a slightly different question: Given that the debt is far beyond what is going to
be offered as repayment, what is the best transfer of output to ask for in the current period?
Nevertheless, we assume that the HIPC initiative implicitly chooses the level of government
expenditure consistent with a principle-agent solution to this period-by-period problem, in some
manner. There is no other obvious way of backing out an estimate of l, since it is difficult to
estimate it independently. Table 1 gives the calibration values for b, h and l, together with the
implied first-best optimal effort levels (bl).
Table 1
Key Calibration Parameters
Benin
Bolivia
Ethiopia
Guyana
Nicaragua
Niger
Sierra Leone
Togo
Central African Rep.
Congo, Dem. Rep.
Sao Tome and Principe
Somalia
b
h
G
eKrug
l
SOC
eHIC
0.2
0.3
0.1
1.0
0.3
0.2
0.2
0.5
0.2
0.2
0.3
0.3
8
12
6
52
15
10
12
25
10
11
19
12
10
14
19
19
19
15
11
11
12
6
30
17
90
86
81
81
81
85
89
89
89
94
70
83
513
334
668
92
264
413
438
204
398
451
284
356
–0.4
–0.3
–0.5
–11.6
–1.9
–0.6
–2.1
–4.4
–0.4
–0.5
–9.0
–1.7
92
87
85
92
86
88
97
97
90
96
92
89
The first column is the slope coefficient from the equation (1) regression.13 The second
column is the maximum absolute time-series residual from these regressions. The third column
is the share of government consumption spending in 1999 (the inaugural year of Enhanced
HIPC), or, for those countries that reached a decision point under the 1996 HIPC initiative, the
average share of government expenditure between the HIPC decision point and completion
point dates.14 The fourth column is the GDP share of non-government expenditure, which equals
100 minus the third column. The fifth column is obtained by taking the expression for the
optimal value of e attainable under the Krugman contract (equation (6)) and setting e equal to
the supposedly optimal level of effort observed in history (the fourth column). Given b and h,
the implied value of l is then calculated.
Can HIPCs Use Hyper-Incentives?
121
As a check of the appropriateness of the model, the sixth column calculates the second
order condition (equation (3)) and the seventh column works out the first-best level of effort
given b and l (equations (7) and (10)). Based on these two tests, a number of countries (not
shown in the table) with positive second order conditions were excluded from further analysis,15
as were any countries that registered first-best optimal shares of private expenditure exceeding
100 per cent.16
Armed with these parameters, the size of the surplus to be divided can be calculated.
Table 2
Calibrated Surplus
(Krug = Krugman, HIC = Hyper-incentive Contract, U = UKrug)
Benin
Bolivia
Ethiopia
Guyana
Nicaragua
Niger
Sierra Leone
Togo
CAR
Congo
Dem.Rep.
Sao Tome
& Principe
Somalia
aKrug
a/bHIC
bHIC
eKrug
eHIC
x/GDP
Krug
x/GDP
HIC
HIC
pay
$US
GDP
DV
$DV
8.1
11.2
5.2
41.2
13.4
9.1
9.9
21.3
10.0
10.1
8.1
11.2
5.2
42.4
13.5
9.1
10.1
21.7
10.0
10.1
1.0010
1.0004
1.0036
1.0246
1.0075
1.0020
1.0155
1.0145
1.0006
1.0013
90
86
81
81
81
85
89
89
89
94
92
87
85
92
86
88
97
97
90
96
16
22
10
81
27
18
20
42
20
20
17
23
11
91
28
19
22
46
20
21
0.01
0.01
0.02
1.20
0.11
0.02
0.18
0.36
0.01
0.01
2700
7800
6060
717
4000
2170
783
1380
1050
5710
0.004
0.003
0.010
0.581
0.054
0.010
0.086
0.173
0.003
0.007
11
20
59
416
217
21
67
238
3
38
12.4
14.0
1.1070
70
92
23
30
1.67
50
0.810
41
10.5
10.6
1.0093
83
89
21
22
0.11
917
0.054
49
The first column is the required repayment of the Krugman contract, given by equation (5).
The second column is the required repayment of the hyper-incentive contract, given by equation
(11). The reason it is higher than the required repayment in the Krugman contract is that the
reservation utility used in the hyper-incentive contract is the utility available to the debtor
under the Krugman contract. That being the case, the extra payment that debtors are expected to
receive from a hyper-incentive payment (the expectation of equation (12)), must be offset with
less forgiveness, to leave them with the same expected utility.17 The third column gives the
hyper-incentive parameter b (equation (11)). Naturally, the comparable ‘parameter’ for the
Krugman contract is just unity. The fourth and fifth columns give the levels of effort under the
Krugman and hyper-incentive contracts (equations (6) and (10)). Corresponding to each of
these effort levels, there is model based predicted ratio of exports, based on the estimated
version of equation (1). The predicted ratios of exports-to-GDP with the Krugman and hyperincentive (first best) effort levels are thus given in columns 6 and 7.
Column 8 evaluates equation (12) at the predicted level of exports using the first best effort
of column 5. This gives the amount (as a share of GDP) that would have to be paid to exporters
under the hyper-incentive contract if the predicted value was the outcome. The US$ amount
can be calculated using the ninth column, which gives the level of GDP for 2002.
122
Gordon Douglas Menzies
The tenth column shows the change in the expected sum of the utilities (V) as we move
from a Krugman contract to a hyper-incentive contract (equation (7)). Given the assumption
that expected utility is unchanged for the debtor (prior to any lump sum transfers) the change in
V is the expected size of the surplus. It is calculated by evaluating equation (7) under both
contracts.
2
ìï
üï ïì
eKrug
e2
ïü
- Lý
DV = íbeHIC - HIC - L ý - íbeKrug 2l
2l
ïî
ïþ ïî
ïþ
2
æ eKrug
e2
- HIC
= b (eHIC - eKrug ) + ç
ç 2l
2l
è
ö
÷
÷
ø
As was noted earlier, these amounts (some of which are not trivial for a developing country)
represent efficiency gains that can be divided up between the creditor and debtor. They average
around $US2002 100 million for each country.
Noteworthy country results are driven by the parameters in the equation for DV, and by the
fact that the last column $DV is measured in $US values. Guyana gains so much from the switch
to a hyper-incentive contract because the impact of changes in government spending on exports
is high (its b in Table 1 is unity, much higher than the values for other countries). Since Guyana
is highly efficient at transforming effort (cuts in government spending) into increases in exports,
then it matters a great deal if effort is not at the optimal level. The other two countries that have
high $DV values, Nicaragua and Togo, have relatively open economies with high export to
GDP ratios. Again, this makes for a large $US value of optimal output.
CONCLUSION
This paper has shown how a hyper-incentive contract could improve upon Krugman’s stylized
debt forgiveness contract. The terms of the contract are not dissimilar to the original contract,
but some efficiency gains are possible.
In making this case, it is argued that debt forgiveness has been pressed into the service of
too many goals. The single instrument of debt forgiveness cannot achieve both the target level
of welfare for the indebted country demanded by the proponents of debt forgiveness, and, the
maximal creditor returns desired by those who want to see these countries improve their reputation
in international capital markets. In principle, the hyper incentive contract could achieve both.
In order to convey these core ideas, a calibration exercise has been undertaken to illustrate
that significant gains (at least on the scale of a poor country budget) are possible. The calibration
exercise has mapped the real world onto a very simple model structure, and it is naturally
limited in a number of respects.
First, a more realistic modeling exercise would involve a multivariate model for exports,
and, a correspondingly more complex contract. Second, a more nuanced measure of reform
effort would be also be desirable, since reducing government spending is a crude, and often
misleading, measure. Social welfare can be strongly influenced by government spending on
Can HIPCs Use Hyper-Incentives?
123
basic services and infrastructure, and so the reductions implied by comparing columns 4 and 7
in Table 1 may be both infeasible and undesirable for particular countries.
Nevertheless, just as real world HIPC debt forgiveness is much more complex than
Krugman’s stripped down model, so it is to be expected that real world hyper-incentive contracts
would likewise require further development. It has been the purpose of this paper to make the
case that that development may be worthwhile.
ACKNOWLEDGEMENT
This research was supported by a Faculty Research Grant from the University of Technology,
Sydney. I wish to thank participants at the 2004 UN Wider conference in Helsinki for useful
feedback, and Kate McKinnon for earlier work, attempting to quantify the cost of adjustment
effort. I am, however, solely responsible for any inadequacies in this paper.
NOTES
1.
For example, Fernandez-Ruiz (1996) uses essentially the same setup as Krugman.
2.
These models implicitly assume that debtors wanted to pay their creditors, even if the debt was
sovereign. This ‘gunboat technology’ sidesteps a major puzzle surrounding sovereign debt – namely,
why is it repaid at all? The literature offers the threat of trade sanctions and financial autarky as
potential explanations (see Eaton 1993). Also, it has been suggested that debtor governments have
multiple relationships, and that appearing untrustworthy in one relationship (by defaulting) will create
difficulties in other relationships (Cole and Kehoe 1998).
3.
What is appropriate depends on many factors, some of which are outside the scope of traditional
economic analysis.
4.
Otherwise, traditional conditionality – if the debtor does A the creditor provides B – is the most
appropriate form of assistance. An example of observable reform effort is floating an exchange rate.
5.
Note that output here could be exports, or government revenue for paying foreign creditors. There is
no requirement at this level of abstraction that it be total GDP, with the implausible implication that
no GDP is consumed until it exceeds L. In the calibration exercise later in the paper effort is nongovernment GDP, based on personal communication with IMF staff, in a meeting to discuss this
model in 2006.
6.
The sign of the partial with respect to b follows from the (unstated) second order condition.
7.
As the formal model is set up, the creditor is residual claimant. However, an alternative modelling
device is that the surplus be transferred to the debtor via a costless lump sum transfer at the end of
period 2.
8.
All data is taken from the World Bank World Development Indicators database, and are expressed in
nominal $US. Since the model variables are ratios, the currency chosen is irrelevant.
9.
The formulation for the calibration exercise must be simple enough to map to the single-variable
theoretical model.
10. The statement is also true under a floating rate; a depreciation increases net exports and the dashed IS
curve returns to its initial position.
11. The list of HIPC countries is taken from Andrews et al., (1999).
12. Again, the mapping onto the analytically tractable model requires a simple distributional assumption.
124
Gordon Douglas Menzies
The Likelihood function is L = (1/2h)n if ei € [h, –h], and = 0 otherwise, where ei is the estimated
residual. Clearly, maximum-likelihood h is reduced (increasing the likelihood) until it equals the
largest absolute residual. Further reductions in h result in the collapse of the likelihood function to
zero.
13. All coefficients are significant at the 1 per cent level, though the estimates are obviously subject to
omitted variable bias. Regressions are run from 1972 to 2002 using annual data from the World
Development Indicators database.
14 These are the dates at which debt relief starts, and ends, under the initial HIPC initiative. Liberia and
Myanmar were excluded because they did not have appropriate data. Apart from the Enhanced HIPC
countries, the government spending was averaged over the following periods: Bolivia 1997-98, Burkina
Faso 1997-2000, Guyana 1998-99, Lao PDR 1998, Mali 1998-99, Mozambique 1998-99 and Uganda
1997-98. Although Somalia did not reach a decision point under the initial HIPC initiative, the 1984
share of government expenditure was used due to data limitations.
15. These countries were Burkina Faso, Cameroon, Chad, Congo, Cote d’Ivoire, Ghana, Honduras, Lao
PDR, Malawi, Mauritania, Senegal, Tanzania, Uganda and Zambia.
16. These countries were Ghana, Madagascar, Mali, Mozambique, Rwanda, Burundi and Sudan.
17. The debtor also exerts more effort under the hyper-incentive contract, but they are rewarded with
more export revenue for this.
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